Why Yom Kippur is Shabbat? Why can't we atone for sins on a work day? Let's take a look:
YLT Lv 23:27 'Only--on the tenth of this seventh month is a day of atonements; ye have a holy convocation, and ye have humbled yourselves, and have brought near a fire-offering to Jehovah;
YLT Lv 23:28 and ye do no work in this self-same day, for it is a day of atonements, to make atonement for you, before Jehovah your God.
YLT Lv 23:29 'For any person who is not humbled in this self-same day hath even been cut off from his people;
YLT Lv 23:30 and any person who doth any work in this self-same day I have even destroyed that person from the midst of his people;
YLT Lv 23:31 ye do no work--a statute age-during to your generations in all your dwellings.
YLT Lv 23:32 It is a sabbath of rest to you, and ye have humbled yourselves in the ninth of the month at even; from evening till evening ye do keep your sabbath.'
As you can tell from the title of this post, the only way for a person not to sin is not to do anything, not to create anything, not to do creative work.
I think, the main reason is why Yom Kippur is on Shabbat, or rather, Yom Kippur is Shabbat, because in order to atone for sin, the first thing you do is stop, rest, take a break from whatever you are doing. Only when your mind is not occupied, you can truly reflect upon yourself and see all the sins you have committed during your labors.
Verse 30 and 32 explicitly say that Yom Kippur is Shabbat and the main point is not to do Slave Work. It is just as important as the humbling of the soul. Afterall, atonement means release and freedom from sin and this means that it can only happen on the day of rest.
I hope now you see importance of the Yom Kippur being a Shabbat. Sometimes the most obvious things are the hardest to see.